BITSAT 2005 Solved Question Paper

Let A and B be two subsets of S . There are following cases to make a subset of S, under the given condition i.e. A∪B=S and A∩B=ϕ
Case I : If set A has no element. The number of ways of selection of 0 element from set S is ‌nC0 .
Case II : If set A has one element. The number of ways of selection of one element from set S is ‌nC1 .
Case III : If set A has two elements. The number of ways of selection of two element from set S is ‌nC2 .
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Case (n) : If set A has n elements. The number of ways of selection of n elements from set S is " nCn .
∴ Total set of A=‌nC0+‌nC1+‌nC2+.....+‌nCn =2n
Total set of A arid B=2n×2n=22n
Required probability =

2n

22n

=

1

2n